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math.CO2011★ 11 cited
On applications of Razborov's flag algebra calculus to extremal 3-graph theory
Victor Falgas-Ravry, Emil R. Vaughan
In this paper, we prove several new Turán density results for 3-graphs with independent neighbourhoods. We show: π(K_4^-, C_5, F_{3,2})=12/49, π(K_4^-, F_{3,2})=5/18, and π(J_4, F_…
math.PR2011
Sharpness in the k-nearest neighbours random geometric graph model
Victor Falgas-Ravry, Mark Walters
Let denote the random geometric graph obtained by placing points in a square box of area according to a Poisson process of intensity 1 and joining each point to its $…
math.CO2011
Minimal weight in union-closed families
Victor Falgas--Ravry
Let Omega be a finite set and let S be a set system on Omega. For x in Omega, we denote by d_{S}(x) the number of members of S containing x. A long-standing conjecture of Frankl st…